The length of a rectangle is 8 mm longer than its width. Its perimeter is more than 32 mm. Let w equal the width of the rectangle.

a. Write an expression for the length in terms of the width.

b. Use expressions for the length and width to write an inequality for the
perimeter, on the basis of the given information.

c. Solve the inequality, clearly indicating the width of the rectangle.

Divide the total pieces by the number of kids:

108 pieces / 9 kids = 12 pieces per kid.

Answer:

x= 108/9

Step-by-step explanation:

Final answer:

The function f(x) = 2x^3 – x^2 – 6x is found by factoring the function, resulting in the zeros at x = 0, x = -3/2, and x = 2.

Explanation:

To find the zeros of the function f(x) = 2x^3 – x^2 – 6x, we must set the function equal to zero and solve for x. If possible, this can be done by factoring the function or using synthetic division. In this case, the function can be factored by taking out a common factor of x:

f(x) = x(2x^2 - x - 6) = 0

Next, we can factor the quadratic equation 2x^2 - x - 6 to find the remaining zeros:

2x^2 - x - 6 = (2x + 3)(x - 2)

This gives us the following zeros for the function:

x = 0

x = -3/2

x = 2

Therefore, f(x) has three zeros: 0, -1.5 (or -3/2), and 2.

Answer:

B. ΔABD, ΔADC, ΔDBC

Step-by-step explanation

Step -1 In ΔABD and ΔADC (from figure).

∠DAB=∠CAD (common in both triangles) ,

∠DBA=∠CDA =90 degree, and

∠BDA=∠DCA (rest angle of the two triangles).

therefore ΔABD similar to ΔADC (by AAA similarity theorem).

Step -2 In ΔDBC and ΔADC (from figure).

∠DCB=∠ACD (common in both triangles) ,

∠DBC=∠ADC =90 degree, and

∠CDB=∠CAD (rest angle of the two triangles).

therefore ΔDBC similar to ΔADC (by AAA similarity theorem).

Step -3 In ΔABD and ΔDBC (from figure).

∠BDA=∠BCD (because , ∠ACD=ADB from stap-1 and ∠ACD=∠BCD from figure) ,

∠DBA=∠CBD =90 degree, and

∠BAC=∠BDC (rest angle of the two triangles).

therefore ΔABD similar to ΔDBC (by AAA similarity theorem).

In the above step- ΔABD similar to ΔADC, ΔDBC similar to ΔADC and ΔABD similar to ΔDBC.

Hence ΔABD, ΔADC, ΔDBC similar to each other in the given figure.

Based on the diagram shown above, the three similar right triangles are: B. ΔABD, ΔADC, ΔDBC.

The Right Triangles Similarity Theorem states that when the altitude of a  triangle is drawn to the hypotenuse of a right angled triangle, then, the two triangles that are formed would be similar to each other, as well as the original triangle.

Based on triangles ABD and ADC, we can logically deduce the following congruent angles;

m∠DAB ≅ m∠CAD

m∠DBA ≅ m∠CDA = 90°

m∠BDA ≅ m∠DCA

ΔABD ~ ΔADC (AAA similarity theorem).

Based on triangles DBC and ADC, we can logically deduce the following congruent angles;

m∠DCB ≅ m∠ACD

m∠DBC ≅ m∠ADC = 90°

m∠CDB ≅ m∠CAD

ΔDBC ~ ΔADC (AAA similarity theorem).

Based on triangles ABD and ΔDBC, we can logically deduce the following congruent angles;

m∠BDA ≅ m∠BCD

m∠DBA ≅ m∠CBD = 90

m∠BAC ≅ m∠BDC

ΔABD ~ ΔDBC (AAA similarity theorem).

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8} \div\frac{3}{2}[/tex]

[tex]\frac{3}{8}\times\frac{2}{3}[/tex]

[tex]\textrm{Multiply the numerator and the denominator.}[/tex]

[tex]3 *2 = 6\\ 3*8=24[/tex]

[tex]\frac{6}{24} =\frac{1}{4}[/tex]

The value of the expression 3/8 divided by 1 and 1/2 is calculated by converting the mixed number into an improper fraction, changing the division to multiplication by using the reciprocal, and simplifying the multiplication to get the final answer, which is 1/4.

The question is asking for the value of the mathematical expression 3/8 divided by 1 and 1/2. To solve this problem, first, we need to convert 1 and 1/2 into an improper fraction.  The result is 3/2. Next, we should remember that division by a number is the same as multiplication by its reciprocal. Therefore, we turn the equation into a multiplication problem by multiplying 3/8 by the reciprocal of 3/2, which is 2/3.

Solving this gives us the answer: (3/8) * (2/3) = 1/4. So, the value of the expression 3/8 divided by 1 and 1/2 is 1/4.

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Answer:

24

Step-by-step explanation:

1/4 * 48 = 12

12 marbles are red.

48 - 12 = 36

36 of the marbles are blue.

Difference = Blue - Red

Difference  = 36 - 12

Difference = 24

Answer:

Around $93.65

Step-by-step explanation:

(1 - 37%)(x) = 59

(0.63)(x) = 59

x = 93.65

Final answer:

To find the original price of the printer before a 37% discount, we set up an equation and solve for the original price. After solving, the original price is found to be approximately $93.65.

Explanation:

To calculate the original price of the printer before the discount, we need to understand that the sale price represents 100% - the discount percentage of the original price. Given that the sale price is $59 after a 37% discount, we set up an equation where the original price (which we'll call P) minus 37% of P equals $59.

The equation looks like this: P - 0.37P = $59. We can simplify this equation by combining like terms, which gives us 0.63P = $59. To find P, we then divide both sides of the equation by 0.63, leading us to the original price.

Let's do the math:

The original price of the printer is calculated to be approximately $93.65.

Answer:

[tex]|m-32|\leq 8[/tex]

Range: [tex]24\leq m\leq 40[/tex]

Step-by-step explanation:

Let m represent cost of medication.

We have been given that a pharmacy claims that the average medication costs $32 but it could differ as much as $8.

[tex]|\text{Actual}-\text{Ideal}|\leq \text{tolerance}[/tex]

[tex]|m-32|\leq 8[/tex]

Using absolute value inequality definition, if [tex]|u|\leq a[/tex], then [tex]-a\leq u\leq a[/tex], we will get:

[tex]-8\leq m-32\leq 8[/tex]

[tex]-8+32\leq m-32+32\leq 8+32[/tex]

[tex]24\leq m\leq 40[/tex]

Therefore, the range of medication costs at the pharmacy is [tex]24\leq m\leq 40[/tex].

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-1}{6-4}=\stackrel{\textit{slope}}{-\cfrac{1}{4}}\implies \cfrac{y-1}{2}=-\cfrac{1}{4} \\\\\\ 4y-4=-2\implies 4y=2\implies y=\cfrac{2}{4}\implies y=\cfrac{1}{2}[/tex]

Answer:

C. 10 units

Step-by-step explanation:

The half diagonals of a rhombus are the legs of a right triangle with the hypotenuse being the side of the rhombus.

EG and FH are the diagonals of the rhombus. The half-diagonals measure 8 and 6.

We can use the Pythagorean theorem to find the hypotenuse length with is the length of the side of the rhombus.

a^2 + b^2 = c^2

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c^2 = 100

c = 10

Answer: 10 units

The length of one side of the rhombus is 10 units.

A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.

Given that,

EFGH is a rhombus.

Length of the two diagonals are also given.

EG = 16 and FH = 12

In a rhombus, the diagonals bisect each other at right angles.

Let the intersection point of the diagonals be O.

Consider ΔOFG.

Using Pythagoras Theorem,

(FG)² = (OG)² + (OF)²

OG = EG / 2 = 16 / 2 = 8

OF = FH / 2 = 12 / 2 = 6

(FG)² = 8² + 6²

        = 100

FG = √100 = 10

Hence the length of one side of the rhombus is 10 units.

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Answer: X=16

Step-by-step explanation: Add 90 and 22 and you will get 112. Since the beginning of the equation is "7x" which is multiplication you use Inverse Operations. So, you divide the sum, 112, by 7. Your answer will be 16.

Answer:

C

Step-by-step explanation:

The measure of angle BC of the triangle is given by BC = 130°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔBCD , where it is isosceles

And , the measure of BC ≅ BD

where Isosceles triangle C B D has points on the circle.

The measure of arc CD = 100°

Now , arc length is twice the inscribed angle.

2 x ∠B = CD

2 x ∠B = 100

∠B = 100/2

∠B = 50

Now, in an isosceles triangle, the angle opposite to the equal sides must be equal.

The sum of the three angles must be 180.

x + x + 50 = 180°

2x = 180 - 150

2x = 130°

Hence , the measure of angle BC = 130°

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Answer:

The range of the graph is all real numbers greater than or equal to 0.

Step-by-step explanation:

we have

[tex]y=\sqrt{x}[/tex]

using a graphing tool

The graph in the attached figure

step 1

Find the domain

we know that the radicand of the function must be greater than or equal to zero

so

The domain is the interval ------> [0,∞)

[tex]x\geq0[/tex]

All real numbers greater than or equal to zero

step 2

Find the range

The range is the interval -----> [0,∞)

[tex]y\geq0[/tex]

All real numbers greater than or equal to zero

The probability of drawing three queens in a row from a standard deck of cards, starting with the first card drawn as a queen and with no replacement, is approximately 0.0181% or 0.000181.

The probability of drawing a queen from a deck of 52 cards, given that the first card drawn was a queen and that cards are not replaced, involves a combination of multiplying probabilities for independent events:

To find the total probability of drawing three queens in a row, we multiply these independent probabilities together: (1/13) * (3/51) * (2/50). This totals to approximately 0.000181, or 0.0181%, which is the probability of drawing three queens in a row from a standard deck of cards without replacement after drawing the first queen.

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Answer:

Option D. (2,0)

Step-by-step explanation:

we know that

The graph show a vertical parabola open upward, the vertex represent a minimum

The vertex is the point (2,0)

The vertex of the graph given is located at the point (0,2)

The vertex of a curve is simply given by the maximum or minimum point on the parabolic curve.

For the graph shown, the vertex is the minimum point on the curve. It also represents the highest or lowest point depending on the function.

Hence, the vertex of the curve is (2, 0)

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Answer:

False

Step-by-step explanation:

The totals of the rows and columns of a two way table are not called marginal distributions. They are called conditional distributions.

Answer:

2.76

Step-by-step explanation:

you only round up if it is a five or higher

Answer:

Step-by-step explanation:

The thousandth digit is a 4. When you round it, it is under 5 so the 4 is dropped and the result is 2.76

Answer:

[tex]\large\boxed{a_n=2\cdot(3)^{n-1}}[/tex]

Step-by-step explanation:

[tex]2,\ 6,\ 18,\ 54,\ 162,\ ...\\\\2\cdot3=6\\6\cdot3=18\\18\cdot3=54\\54\cdot3=162\\\vdots\\\\\text{It's a geometric series with common ratio}\ r=3,\ \text{and the first term}\ a_1=2.\\\\\text{The explicit formula of a geometric sequence:}\ a_n=a_1r^{n-1}.\\\\\text{Substitute:}\\\\a_n=2\cdot(3)^{n-1}[/tex]

Final answer:

The explicit formula for the sequence 2, 6, 18, 54, 162, ... is [tex]an = 2 imes 3^(n-1),[/tex] where an represents the nth term of the sequence.

Explanation:

The sequence given is 2, 6, 18, 54, 162, ..., which can be recognized as a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio (r). To find the explicit formula for the nth term of a geometric sequence, we use the formula an = a1  imes r(n-1), where a1 is the first term and r is the common ratio.

Looking at our sequence, the first term a1 is 2. The common ratio r can be found by dividing the second term by the first term (or any term by the previous term), which is 6/2 = 3. Now that we have both the first term and the common ratio, we can plug these values into our formula to get the explicit formula for the nth term of the sequence: an = 2  imes 3(n-1).

Answer:

10

Step-by-step explanation:

Answer: the answer is 10

Step-by-step explanation:  i took the test and got it right

Answer:

$82,250 < x <= $171,550

Step-by-step explanation:

You didn't provide all the possible answers.  In this case we don't need to see all answers to help you... but because you didn't provide all the choices for answer, we can't give the exact answer, only the possible range of values.

The question asks for a possible taxable income for someone filing under the 28% bracket.

If we look at the table, we see the 28% bracket is for income ranging from $82,250 (exclusively) to $171,550 (inclusively)

So, your answer has to be within the range:

$82,250 < x <= $171,550

It cannot be $82,250 but it can be $171,550 and any number in between.

Since you didn't provide all the answer choices, we can't tell you if it's B, C, D, and so on... but we can tell you it's not A.

Step-by-step answer:

The domain of log functions (any legitimate base) requires that the argument evaluates to a positive real number.

For example, the domain of log(4x) will remain positive when x>0.

The domain of log_4(x+3) requires that x+3 >0, i.e. x>-3.

Finally, the domain of log_2(x-3) is such that x-3>0, or x>3.

Answer:

all real numbers greater than –3

Step-by-step explanation:

interval notation wise, yes, because x < 2 means, x less than 2, not equals to 2, but less, so "x" is anything that is less than 2, not 2 itself, but anything less.

[tex]\bf \stackrel{~\hfill \rule[2pt]{8em}{0.25pt}\circ}{\rule[0.35em]{10em}{0.25pt}}2\rule[0.35em]{10em}{0.25pt}[/tex]

Answer:

(x - 2)² + (y - 3)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (2, 3) and r = 3, hence

(x - 2)² + (y - 3)² = 9 ← equation of circle

Answer:

18

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

Step-by-step explanation:

If from a table a ratio

[tex]\dfrac{y_2-y1}{x_2-x_1}[/tex]

is constant, then a table represents a linear function.[tex]\begin{array}{c|c}x&y\\1&-2\\2&-10\\3&-18\\4&-26\end{array}\\\\\dfrac{-10-(-2)}{2-1}=\dfrac{-8}{1}=-8\\\dfrac{-18-(-10)}{3-2}=\dfrac{-8}{1}=-8\\\dfrac{-26-(-18)}{4-3}=\dfrac{-8}{1}=-8[/tex]

[tex]\begin{array}{c|c}x&y\\1&-2\\2&-4\\3&-8\\4&-16\end{array}\\\\\dfrac{-4-(-2)}{2-1}=\dfrac{-2}{1}=-2\\\dfrac{-8-(-4)}{3-2}=\dfrac{-4}{1}=-4[/tex]

Step-by-step explanation:

If (p, 0) and (q, 0) are x-intercepts, then p and q are zeros.

The intercept form of an equation of a quadratic function:

y = a(x - p)(x - q)

p, q - x-intercepts (zeros).

We have the equation: y = 2(x + 4)(x - 6) = 2(x - (-4))(x - 6)

Therefore the x-intercepts are -4 and 6.

The zeros are -4 and 6 too.

Answer:

2.75s + 2w ≤ 15  

3 waters  

2.75s + 2(3) ≤ 15  

2.75 + 6 ≤ 15  

Subtract 6 from both sides  

2.75s ≤ 9  

Divide both sides by 2.75  

s ≤ 3.27  

since you can't by a negative amount of soda  

0 ≤ s ≤ 3.27  

But you also can't buy part of a soda  

0 ≤ s ≤ 3 <------

Hope this helps?

Inequality which represents the number of sodas is 0 ≤ s ≤ 3.

Given:

Alexandra has $15.

Cost of soda = $2.75

Cost of bottled water = $2.00

2.75s + 2w ≤ 15

Let, number of sodas be s.

number of bottled water be w.

Three Alexandra's friends asked for water.

∴ w = 3

⇒ 2.75s + 2(3) ≤ 15

⇒ 2.75s + 6 ≤ 15

Subtracting 6 from the both sides, we get:

⇒ 2.75s ≤ 15 - 6

⇒ 2.75s ≤ 9

Divide both sides by 2.75, we get:

⇒ s ≤ 9/2.75

⇒ s ≤ 3.27

But the number of sodas (s) should be a whole number and not an integer.

⇒ s ≤ 3

⇒ 0 ≤ s ≤ 3

Therefore, the inequality which represents the number of sodas she can

buy is 0 ≤ s ≤ 3.

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Answer: [tex]\dfrac{9}{10}[/tex]

Step-by-step explanation:

From the table , the total number of numbers = 10

The group of 5 digits contain less than or equal to 2 even digits = 55170

i.e. The total group of 5 digits contain at least 2 =[tex]10-1=9[/tex]

Now, the probability that a group of 5 random digits will contain at least 2

even digits is given by :-

[tex]=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}=\dfrac{9}{10}[/tex]

Hence, the probability that a group of 5 random digits will contain at least 2  even digits [tex]=\dfrac{9}{10}[/tex]

Answer:

the answer is 9/10

Step-by-step explanation:

Answer:

(x + 3)(x + 7)

Step-by-step explanation:

Find two numbers that when added up to , they ALSO have to multiply up to 21. This is simple because of the fact that there is no leading coefficient greater than 1⃣.

Answer:

A.) (x+3)(x+7)

Step-by-step explanation:

Answer:

Last option

Step-by-step explanation:

Given expression is:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5} }[/tex]

The terms can be simplified one by one

[tex]=\sqrt{\frac{64x^5y^6}{x^7y^5} }[/tex]

As the larger power of x is in numerator, the smaller power will be brought to denominator

[tex]=\sqrt{\frac{64y^6}{x^{(7-5)}y^5}}\\=\sqrt{\frac{64y^6}{x^{2}y^5}}[/tex]

Similarly for y,

[tex]=\sqrt{\frac{64y^{(6-5)}}{x^{2}}}\\=\sqrt{\frac{64y}{x^{2}}}[/tex]

Applying the radical

[tex]\sqrt{\frac{8^2*y}{x^{2}}}\\So\ the\ answer\ will\ be\\= \frac{8\sqrt{y}}{x}[/tex]

So, last option is the correct answer ..

Answer: Last option.

Step-by-step explanation:

You need to apply the Quotient of powers property:

[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]

Then:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}} =\sqrt{\frac{64y}{x^2}}[/tex]

Remember that:

[tex]64=8*8=8^2[/tex]

Then you can rewrite the expression:

[tex]=\sqrt{\frac{8^2y}{x^2}}[/tex]

Finally, since [tex]\sqrt[n]{a^n}=a[/tex], you get:

[tex]=\frac{8\sqrt{y} }{x}[/tex]

Answer:

Step-by-step explanation:

Mark the given points in the coordinate system (look at the picture).

Find the point D.

Other solutions:

D(-5, 8)

D(7, -2)

Look at the other pictures

If you want calculate it, then:

The vectors AB and DC are congruent and the vectors BC and AD are congruents too.

If a vector ,< a, b > is congruent to a vector < c, d >, then a = c and b = d.

The formula of coordinates of the vetror:

< x₂ - x₁, y₂ - y₁ >

We have A(-2, 4), B(1, 3), C(4, -1) and D(x, y). Substitute:

vector AB = < 1 - (-2), 3 - 4 > = < 3, -1 >

vector DC = < 4 - x, -1 - y >

vector BC = < 4 - 1, -1 - 3 > = < 3, -4 >

vector AD = < x - (-2), y - 4 > = < x + 2, y - 4 >

Therefore we have the equations:

AB = DC ⇒ 4 - x = 3 and -1 - y = -1 ⇒ x = 1 and y = 0

BC = AD ⇒ x + 2 = 3 and y - 4 = -4 ⇒ x = 1 and y = 0